CHAPTER 6 - COUNTING TECHNIQUES; PERMUTATIONS AND COMBINATIONS

Abstract

This chapter describes the concepts of permutations and combinations. Given a set of distinct objects, an arrangement of these objects in a definite order without repetitions is called a permutation of the set. In general, a permutation of r objects selected from a set of n objects is called a permutation of the n objects taken r at a time. The number of permutations of a set with n distinct objects is n(n−l)(n−2)….1. The number n(n−l)(n−2)….1 is designated by the symbol n!. A subset of r objects selected from a set of n objects is called a combination of the n objects taken r at a time. In counting problems, it should be kept in mind that if order matters, permutations should be used and if order does not matter, combinations should be used. The multiplication principle tates that if there are k ways to make a decision D1 and then n ways to make a decision D2, then there are kn ways to make the two decisions D1 and D2.